Kinetic Transition Networks for the Thomson Problem and Smale’s Seventh Problem

Abstract

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Magic numbers for vibrational frequency of charged particles on a sphere

“…As a model, we consider N charges on a unit sphere that is a platform in the Thomson problem and/or the Smale's seventh problem [6]: to determine the minimum energy configuration of N charges confined to the surface of a unit sphere. The global and local minima of the PES have been investigated for this system [7][8][9][10][11][12], while many related problems have also been studied [13][14][15][16][17]. Through the total energy calculations for N ≤ 200, N = 12, 32, 72, 122, 132, 137, 146, 182, 187, and 192 have been identified to be magic numbers [7].…”